Omar is 12 years older than Vanessa. Two years ago, Omar was 5 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Omar and Vanessa. Let Omar's current age be $o$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $o = v + 12$ Two years ago, Omar was $o - 2$ years old, and Vanessa was $v - 2$ years old. The information in the second sentence can be expressed in the following equation: $o - 2 = 5(v - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $o$ and substitute it into our second equation. Our first equation is: $o = v + 12$ . Substituting this into our second equation, we get the equation: $(v + 12)$ $-$ $2 = 5(v - 2)$ which combines the information about $v$ from both of our original equations. Simplifying both sides of this equation, we get: $v + 10 = 5 v - 10$ Solving for $v$ , we get: $4 v = 20$ $v = 5$.